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If you have the following data about a
box of crackers, about how many
crackers are estimated to be in the
box?
Mass of Crackers + Box = 924 grams
Mass of 27 Crackers = 24 grams
Mass of Box ONLY = 328 grams
How many crackers are in the box?
Round your answer by using
significant figures.

If you have the following data about a box of crackers about how many crackers are estimated to be in the box Mass of Crackers Box 924 grams Mass of 27 Crackers class=

Respuesta :

msm555

Answer:

672 crackers

Step-by-step explanation:

To find the estimated number of crackers in the box, we can first determine the mass of the crackers alone by subtracting the mass of the box from the total mass of crackers and the box.

Given:

  • Mass of crackers + box = 924 grams
  • Mass of box only = 328 grams

We can find the mass of crackers alone by subtracting the mass of the box from the total mass:

[tex] \textsf{Mass of crackers} = \textsf{Mass of crackers + box} - \textsf{Mass of box} \\\\ = 924 \, \textsf{g} - 328 \, \textsf{g} \\\\ = 596 \, \textsf{g} [/tex]

Next, we are given that the mass of 27 crackers is 24 grams. To find the mass of one cracker, we can divide the mass of 27 crackers by 27:

[tex] \textsf{Mass of one cracker} = \dfrac{\textsf{Mass of 27 crackers}}{27}\\\\ = \dfrac{24 }{27}\, \textsf{g} [/tex]

Finally, to estimate the number of crackers in the box, we can divide the mass of crackers alone by the mass of one cracker:

[tex] \textsf{Number of crackers} = \dfrac{\textsf{Mass of crackers}}{\textsf{Mass of one cracker}} \\\\ = \dfrac{596 \, \textsf{g}}{\dfrac{24}{27} \, \textsf{g}} \\\\\approx \dfrac{596 \times 27}{24} \\\\ = 670.5 \, \textsf{crackers} [/tex]

Rounding to the nearest whole number, we estimate that there are approximately 672 crackers in the box.

semsee45

Answer:

671 crackers (3 s.f.)

670 crackers (2 s.f.)

Step-by-step explanation:

To calculate the number of crackers in the box, we need to subtract the mass of the box from the mass of the crackers + box to give us the mass of the total number of crackers, then divide the result by the mass of one cracker.

Given that the mass of 27 crackers is 24 grams, the mass of one cracker is the number of grams divided by the number of crackers:

[tex]\textsf{Mass of one cracker}=\dfrac{24}{27}\; \sf grams[/tex]

Now, subtract the mass of the box from the mass of the crackers + box, and divide it by the mass of one cracker:

[tex]\textsf{Number of crackers in the box}=\dfrac{924-328}{\frac{24}{27}}\\\\\\\textsf{Number of crackers in the box}=\dfrac{596}{\frac{24}{27}}\\\\\\\textsf{Number of crackers in the box}=596 \times \dfrac{27}{24}\\\\\\\textsf{Number of crackers in the box}=\dfrac{16092}{24}\\\\\\\textsf{Number of crackers in the box}=670.5[/tex]

To round 670.5 to the nearest whole number, we round to three significant figures. In this case, we round up to 671 because the digit following the third significant figure is 5 or greater.

Therefore, the estimated number of crackers in the box rounded to 3 significant figures is:

[tex]\LARGE\boxed{\boxed{671\; \sf crackers}}[/tex]

Additional Notes

If we want to round to 2 significant figures, the result would be 670 crackers.

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